Functions Quiz 1

Question 1

If $$f$$ is a function defined by  $$ \ f(x) = 2x + 8,\;x \leqslant 2 \  \;\;\;\;\;\;\;\;\;2x - 2,\;\;x \geqslant 2 \  $$ Find $$f\left( 0 ight), f\left( 2 ight)$$ and $$ f\left( 4 ight).$$

Accepted Answer

$$8,12,6$$

Answer

$$8,12,7$$

Answer

$$8,10,6$$

Answer

$$6,12,6$$

Question 2

If $$f$$ and $$g$$ are defined by; $$f(x) = 4x + 4 \ g(x) = \sqrt {x + 5} \ $$ Find $$fog(4)$$

Accepted Answer

$$16$$

Answer

$$14$$

Answer

$$8$$

Answer

$$10$$

Question 3

Evaluate the value of $$g\left[ {f\left( x \right)} \right]$$ if the value of $$f\left( x \right) = \dfrac{{x + 3}}{{4x + 5}}$$ and $$g\left( x \right) = {\left( {x + 1} \right)^2}$$

Accepted Answer

$${\left[ {\dfrac{{5x + 8}}{{4x + 5}}} \right]^2}$$

Answer

$${\left[ {\dfrac{{4x + 5}}{{5x + 8}}} \right]^2}$$

Answer

$$\dfrac{{{x^2} + 2x + 8}}{{16{x^2} + 14x + 25}}$$

Answer

$$\dfrac{{4{x^2} + 16x + 4}}{{8{x^2} + 15x + 25}}$$

Question 4

Check the correct option from given $$f\left( x ight) = sgm\left[ {x + 1} ight]$$ in $$R 	o R$$

Accepted Answer

Neither injective nor surjective function

Answer

Injective function

Answer

Subjective function

Answer

Objective function

Question 5

Evaluate the value of $${f^{ - 1}}\left( x \right)$$ if the value of $$f\left( x \right) = {e^{{x^2} + 2x + 1}}$$

Accepted Answer

$$\sqrt {\log x}  - 1$$

Answer

$$\sqrt {{x^2} + 2x + 1}  - \log x$$

Answer

$$2x - \log x$$

Answer

$$2\sqrt {\log x}  - 1$$