Free Printable Inverse and Composite Function

1.

Defined function $f:R\rightarrow R$ and $g:R\rightarrow R$ where $f\left(x\right)=x^2-x+3$ and $g\left(x\right)=1-2x$ then $\left(f\circ g\right)\left(x\right)=...$

a)

$4x^2+6x+3$

b)

$4x^2+2x+3$

c)

$4x^2-2x+3$

d)

$-2x^2+2x+5$

e)

$-2x^2-x+5$

2.

Known function $f\left(x\right)=6x-3$ , $g\left(x\right)=5x+4$ and $\left(f\circ g\right)\left(a\right)=81$ . The value of $a$ is…

a)

3

b)

2

c)

1

d)

-1

e)

-2

3.

If $f\left(x\right)=x^3+2$ and $g\left(x\right)=\frac{2}{x-1}$ then $\left(g\circ f\right)\left(x\right)=...$

a)

$2\left(x^3+2\right)\left(x-1\right)$

b)

$\frac{2\left(x^3+2\right)}{x-1}$

c)

$\frac{2\left(x^3+2\right)}{2\left(x-1\right)}$

d)

$\frac{2}{x^3+1}$

e)

$\frac{2}{x^3-1}$

4.

Known that $\left(f\circ h\right)\left(x\right)=5+4x-20x^2$ and $f\left(x\right)=4x-3$ . The value of $h\left(-4\right)$ is equal to…

a)

-82

b)

-81

c)

78

d)

80

e)

86

5.

Defined $f\left(x\right)=3x+7$ and $g\left(x\right)=\sqrt[]{x+15}$ . Value of $\left(f\circ g\right)\left(1\right)=...$ is equal to…

a)

7

b)

12

c)

14

d)

19

e)

23

6.

Function $p:R\rightarrow R$ and $q:R\rightarrow R$ defined with $q\left(x\right)=x+2$ and $\left(f\circ g\right)\left(x\right)=x^2+4x$ . Formula of $p\left(x\right)$ is...

a)

$x^2-12$

b)

$x^2-4$

c)

$x^2-8x+12$

d)

$x^2+2x-4$

e)

$x^2+4x+\text{4}$

7.

Known that $f\left(x+1\right)=x^2-1$ and $g\left(x\right)=2x$ then $\left(g\circ f\right)\left(x\right)=...$

a)

$x^2-4x$

b)

$2x^2-2$

c)

$2x^2+2$

d)

$2x^2-2x$

e)

$2x^2-4x$

8.

If $f\left(x\right)=\frac{2x+1}{x-3},x\ne3$ then inverse function $f\left(x\right)$ is…

a)

$\frac{x-3}{2x+1},x\ne-\frac{1}{2}$

b)

$\frac{2x-3}{x+1},x\ne-1$

c)

$\frac{2x+3}{x-1},x\ne1$

d)

$\frac{3x-1}{x+2}.x\ne-2$

e)

$\frac{3x+1}{x-2},x\ne2$

9.

If $f\left(x-5\right)=\frac{x+2}{x}$ then $f^{-1}\left(x\right)=...$

a)

$\frac{-5x+7}{x-1}$

b)

$\frac{2}{x-1}$

c)

$\frac{x-3}{x+5}$

d)

$\frac{x+7}{x+5}$

e)

$\frac{5x-3}{x-1}$

10.

Known that $g\left(x-1\right)=\frac{x-1}{2x-1},x\ne-\frac{1}{2}$ and $g^{-1}\left(x\right)$ is inverse function $g\left(x\right)$ . Formula of $g^{-1}\left(2x-1\right)=...$

a)

$\frac{x-1}{2x+1},x\ne-\frac{1}{2}$

b)

$\frac{x+1}{2x-4},x\ne2$

c)

$\frac{-x-2}{2x+1},x\ne-\frac{1}{2}$

d)

$\frac{-2x+1}{4x+3},x\ne-\frac{3}{4}$

e)

$\frac{-2x+1}{4x-3},x\ne\frac{3}{4}$

11.

If $f^{-1}\left(x\right)=\frac{x-1}{5}$ and $g^{-1}\left(x\right)=\frac{3-x}{2}$ then the value of $\left(f\circ g\right)^{-1}\left(6\right)=...$

a)

-2

b)

-1

c)

1

d)

2

e)

3

12.

Known that inverse function $g\left(x\right)$ is $g^{-1}\left(x\right)=6-7x$ . The value of $g\left(2\right)=...$

a)

$-\frac{5}{7}$

b)

$-\frac{4}{7}$

c)

$\frac{4}{7}$

d)

$\frac{5}{7}$

e)

$\frac{8}{7}$

13.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=2x-1$ then $\left(g^{-1}\circ f^{-1}\right)\left(x\right)=...$

a)

$\frac{2x-1}{x}$

b)

$\frac{x}{2x-1}$

c)

$\frac{x-1}{2x}$

d)

$\frac{x+1}{2x}$

e)

$\frac{2x}{x-1}$

14.

Function $f$ and $g$ from R to R determined by $f\left(x\right)=1+\frac{1}{x},x\ne0$ and $g\left(x\right)=2x-4$ . Value of $\left(f^{-1}\circ g^{-1}\right)\left(6\right)$ is equal to…

a)

0

b)

$\frac{1}{6}$

c)

$\frac{1}{4}$

d)

$\frac{1}{3}$

e)

$\frac{1}{2}$

15.

Function $p:R\rightarrow R$ and $q:R\rightarrow R$ formulated with $p\left(x\right)=\frac{1}{2}x-1$ and $q\left(x\right)=2x+4$ . The value of $\left(q\circ p\right)^{-1}\left(10\right)=...$

a)

4

b)

8

c)

9

d)

12

e)

16

Inverse and Composite Function

Total questions: 15

Worksheet time: 45mins

Similar Resources on Wayground