Functions I - Ambitious

Question 1: Which of the functions is one-to-one?

A

f (x) = x^{2}, {x \in ℝ}

B

f (x) = \sin x, {x : - π \leq x \leq π}

C

f (x) = \cos x, {x : - \frac{π}{2} \leq x \leq \frac{π}{2}}

D

f (x) = x^{2}, {x : 0 \leq x \leq + \infty}

Question 2: Which of the functions is many-to-one?

A

f (x) = \sin x, {x : \frac{π}{2} \leq x \leq \frac{3}{2} π}

B

f (x) = \tan x, {x : π < x < 2 π}

C

f (x) = \sin x, {x : \frac{3}{2} π < x < \frac{5}{2} π}

D

f (x) = \tan x, {x : 0 \leq x \leq π}

Question 3: Find the inverse of the function

f (x) = x^{2} - 3, x \geq 0

A

f^{- 1} (x) = \frac{3}{x}

B

f^{- 1} (x) = \sqrt{x} + 3

C

f^{- 1} (x) = \frac{1}{x} + 3

D

f^{- 1} (x) = \sqrt{x + 3}

Question 4: Find the inverse of the function

f (x) = {0.3}^{x}

A

f^{- 1} (x) = x^{0.3}

B

f^{- 1} (x) = \frac{0.3}{x}

C

f^{- 1} (x) = 0.3 \log x

D

f^{- 1} (x) = \log_{0.3} x

Question 5: Find

g (f (3))

, where

f (x) = \frac{1}{3} x^{2}, g (x) = 2 x + 3

A

g (f (3)) = 15

B

g (f (3)) = 9

C

g (f (3)) = 27

D

g (f (3)) = 6

Test: Functions I - Ambitious