Singapore GCE A-Level · H2 Mathematics

Functions

33 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 33 questions

The functions $f$ and $g$ are defined by $f (x) = 2 x + 3$ and $g (x) = x^{2} + 5$ . Find the value of $f g (2)$ .
The functions $f$ and $g$ are defined by $f (x) = 3 x - 1$ and $g (x) = x^{2} + 4$ . Find the value of $f g (2)$ .
The functions $f$ and $g$ are defined by $f (x) = 4 x + 1$ and $g (x) = x^{2} + 2$ . Find the value of $f g (2)$ .
The functions $f$ and $g$ are defined by $f (x) = 5 x + 2$ and $g (x) = x^{2} - 3$ . Find the value of $f g (2)$ .
The functions $f$ and $g$ are defined by $f (x) = 2 x - 4$ and $g (x) = x^{2} + 7$ . Find the value of $f g (2)$ .
The functions $f$ and $g$ are defined by $f (x) = 3 x + 2$ and $g (x) = x^{2} + 1$ . Find the value of $f g (2)$ .
The function $f$ is defined by $f (x) = 2 x + 3$ . Find $f^{- 1} (11)$ .
The function $f$ is defined by $f (x) = 3 x - 1$ . Find $f^{- 1} (11)$ .
The function $f$ is defined by $f (x) = 4 x + 5$ . Find $f^{- 1} (11)$ .
The function $f$ is defined by $f (x) = 5 x - 2$ . Find $f^{- 1} (11)$ .
The function $f$ is defined by $f (x) = 2 x - 7$ . Find $f^{- 1} (11)$ .
The function $f$ is defined by $f (x) = 3 x + 4$ . Find $f^{- 1} (11)$ .
The function $f$ is defined by $f (x) = (x - 2)^{2} + 3$ for $x \geq 2$ . Find the range of $f$ .
The function $f$ is defined by $f (x) = (x - 1)^{2} + 5$ for $x \geq 1$ . Find the range of $f$ .
The function $f$ is defined by $f (x) = (x - 3)^{2} - 2$ for $x \geq 3$ . Find the range of $f$ .
The function $f$ is defined by $f (x) = (x - 4)^{2} + 1$ for $x \geq 4$ . Find the range of $f$ .
The function $f$ is defined by $f (x) = (x - 2)^{2} - 1$ for $x \geq 2$ . Find the range of $f$ .
The function $f$ is defined by $f (x) = (x - 5)^{2} + 2$ for $x \geq 5$ . Find the range of $f$ .
The function $f (x) = (x - 1)^{2} + 2$ is defined for $x \geq a$ . State the least value of $a$ for which $f$ has an inverse.
The function $f (x) = (x - 2)^{2} + 3$ is defined for $x \geq a$ . State the least value of $a$ for which $f$ has an inverse.
The function $f (x) = (x - 3)^{2} + 1$ is defined for $x \geq a$ . State the least value of $a$ for which $f$ has an inverse.
The function $f (x) = (x - 4)^{2} + 5$ is defined for $x \geq a$ . State the least value of $a$ for which $f$ has an inverse.
The function $f (x) = (x + 1)^{2} + 4$ is defined for $x \geq a$ . State the least value of $a$ for which $f$ has an inverse.
State the largest possible real domain of $f (x) = 2 x - 1$ .
State the largest possible real domain of $f (x) = 3 x - 6$ .
State the largest possible real domain of $f (x) = 1 x - 4$ .
State the largest possible real domain of $f (x) = 4 x - 8$ .
State the largest possible real domain of $f (x) = 5 x - 10$ .
State the largest possible domain of $f (x) = ln (2 x - 1)$ .
State the largest possible domain of $f (x) = ln (3 x - 4)$ .
State the largest possible domain of $f (x) = ln (1 x - 5)$ .
State the largest possible domain of $f (x) = ln (4 x - 2)$ .
State the largest possible domain of $f (x) = ln (5 x - 3)$ .

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