# SOLUTIONS OF THE FUNCTION QUESTIONS

## High school mathematics lesson. To find the composite of functions. Inverse functions. Operations on functions. The functions test-1 solutions.

Solution 1

f(2x + 10) = 6x + 14

We must do x the 2x + 1 expression for to find the f(x), from the f(2x + 1).

We must take the inverse of this expression for to do x the 2x + 1 expression.

y = 2x + 10

x = 2y + 10

x – 10 = 2y

 y = x – 10 2

If we write this expression instead of all x in the function f(2x + 10) , we finds the function f(x).

f(2•x – 10
 +10) = 6• x – 10) + 14 2

f(x – 10 + 10) = 3x – 30 + 14

f(x) = 3x – 16

The right answer is option B

Solution 2

f(x) = 12x – 36

We can write this function in the following form.

y = 12x – 36

x = 12y – 36

x + 36 = 12y

 y = x + 36 12

 f-1(x) = x + 36 12

The right answer is the option C.

Solution 3

We can write the function f(x) = 16x + 24 as the following.

y = 16x + 24

x = 16y + 24

x – 24 = 16y

 y = x – 24 16

 f-1(x) = x – 24 16

The right answer is option A.

Solution 4

 f(x) = 12x - 8 5

 y = 12x - 8 5

 x = 12y - 8 5

5x = 12y – 8

5x + 8 = 12y

 y = 5x + 8 12

The right answer is option E.

Solution 5

The inverse of inverse of a function is equal to it.

[f(x)-1]-1 = f(x)

 f-1(x) = x + 9 4

If we take inverse of this function, we get the function f(x).

Suppose, f-1 (x) = y .

 y = x + 9 4

Let we write x instead of y and y instead of x.

 x = y + 9 4

4x = y + 9

4x – 9 = y

f(x) = 4x – 9

x = 5 için,

f(5) = 4•5 – 9

f(5) = 11

The right answer is option D.

Solution 6

f(x) = 6x2 + 4

g(x) = 5x + 3

[f + g](x) = f(x) + g(x)

[f + g](x) = 6x2 + 4 + 5x + 3

[f + g](x) = 6x2 + 5x + 7

[f + g](3) = 6•32 + 5•3 + 7

[f + g](3) = 76

[f – g](x) = f(x) – g(x)

[f – g](x) = 6x2 + 4 – 5x – 3

[f – g](x) = 6x2 – 5x + 1

[f – g](1) = 6 – 5 + 2

[f – g](1) = 2

[f + g](3)
 = 76 2
[f – g](1)

= 38

The right answer is option D

Solution 7

To find the composition of the f(x) and g(x) functions, we write the function g(x) instead of x that in the function f(x).

f(x) = 3x + 24

g(x) = 5x – 8

fog(x) = 3(5x – 8) + 24

fog(x) = 15x – 24 + 24

fog(x) = 15x

The right answer is option C

Solution 8

f(x) = x2 – 4x

g(x) = x + 2

We must find the function fog(x), firstly. Then, we takes inverse of this composite function.

We can compute the desired value by typing x = 21, in the inverse function.

fog(x) = (x + 2)2 – 4(x + 2)

fog(x) = x2 + 4x + 4 – 4x – 8

fog(x) = x2 – 4

Now, let we find inverse of this function.

y = x2 – 4

x →y

x = y2 - 4

y2 = x + 4

y = √x + 4

x = 21 için,

y = √4 + 21

y = 5

The right answer is the option B

Solution 9

[gof](x + 6) = 5x + 11

f-1 (x) = x + 1

Firstly, let we find gof(x) function. Then, we can find function f(x). Finally, we can find function g(x) from gof(x) using the function f(x).

y = x + 6

x = y + 6

y = x – 6

If we write x – 6 instead of x in the function gof(x + 6), we get the function gof(x).

gof(x – 6 + 6) = 5(x – 6) + 11

gof(x) = 5x – 19

Now, let we find the function f(x). The inverse of inverse of a function is equal to it. To find the function f(x), we must find inverse of the function f-1 (x).

f-1 (x) = x + 1

y = x + 1

x = y + 1

y = x – 1

f(x) = x – 1

gof(x) = 5x – 19

g(f(x)) = 5x – 19

g(x – 1) = 5x – 19

To get the function g(x), we must take inverse of the x – 1 expression. Inverse of (x – 1) is x + 1. We write this expression instead of x in the function g(x – 1).

g(x + 1 – 1) = 5(x + 1) – 19

g(x) = 5x + 5 – 19

g(x) = 5x – 14

For x = 5,

g(5) = 5•5 – 14

= 11

The right answer is option B

Solution 10

 f(x) = 5x+2 3x+16

 y = 5x+2 3x+16

 x = 5y+2 + 3y+16

3xy + 16x = 5y + 2

5y – 3xy = 16x – 2

y(5 – 3x) = 16x – 2

 y = 16x – 2 5 – 3x

 f-1(x) = 16x – 2 5 – 3x

x = 3 için,

 f-1(2) = 16•2 -2 5-3•2

f-1 (2) = - 30

The right answer is option E

Solution 11

fog(x) = 6x2 – 4

f(x) = 2x + 6

fog(x) = f(g(x))

f(g(x)) = 2g(x) + 6

6x2 – 4 = 2g(x) + 6

6x2 – 10 = 2g(x)

g(x) = 3x2 – 5

The right answer is option C

Solution 12

f(x + g(x)) = x2 + 6

Also,

g(2) = 12

for x = 2,

f(2 + g(2)) = 22 + 6

f(2 + 12) = 4 + 6

f(14) = 10

f-1(10) = 14

The right answer is option E

The Questions

Inverse Functions

Compound Functions

RISE KNOWLEDGE

07/10/2018

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