Combining and composing functions Quiz 1

Question 1

Let $$f:Q 	o Q$$ be a function defined as $$f\left( x ight) = {x^2} + 2$$, then $${f^{ - 1}}\left( {18} ight) = $$

Accepted Answer

$$\left\{ { - 4,\;4} \right\}$$

Answer

$$f$$

Answer

$$\left\{ 4 \right\}$$

Answer

$$\left\{ {} \right\}$$

Question 2

If $$f\left( {g\left( x \right)} \right) = x,$$ then $$g\left( x \right) = $$

Accepted Answer

$${f^{ - 1}}\left( x \right)$$

Answer

$$f\left( x \right)$$

Answer

$$1$$

Answer

None of these

Question 3

If $$h\left( x \right) = 5x$$ and $$k\left( x \right) = 3x - 8$$ then what is $$h\left( {k\left( x \right)} \right)?$$

Accepted Answer

$$15x - 40$$

Answer

$$15x - 8$$

Answer

$$5{x^2} - 8x$$

Answer

$$15{x^2} - 40x$$

Question 4

If $$f\left( x \right) = {x^4}$$ and $$g\left( x \right) = \sqrt x $$ then find $$g\left( {f\left( 3 \right)} \right)$$

Accepted Answer

$$9$$

Answer

$$3$$

Answer

$$27$$

Answer

$$81$$

Question 5

Inverse of the function $$f\left( x \right) = {x^2} - 4$$ is

Accepted Answer

Both (a) and (b)

Answer

$$\sqrt {x + 4} $$

Answer

$$ - \sqrt {x + 4} $$

Answer

$$\sqrt x  + 2$$