Domain and range of f(x)=\sqrt{2-x}?

Domain: x\le2. Range: f(x)\ge0.

The value of C (e.g. cost) for the input n (e.g. number of items).

What does an inverse function do?

It reverses (undoes) the effect of f.

Notation for the inverse of f?

f^{-1}(x) (not \frac{1}{f(x)}).

How is the graph of f^{-1} related to the graph of f?

It is the reflection of the graph of f in the line y=x.

Steps to find f^{-1}(x)?

Write y=f(x), swap x and y, rearrange for y.

Which functions have an inverse?

One-to-one functions: each output comes from only one input.

Why does f(x)=x^2 (all real x) have no inverse?

It is not one-to-one: f(-2)=f(2)=4.

2.2 Concept of a function, domain, range and inverseIB Maths: Applications and Interpretation SL: Flashcards

Card 1 of 130 of 13 known

Question

What is a function?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

What is a function?: A rule that gives exactly one output for each input.
Domain and range?: Domain: the set of allowed inputs. Range: the set of outputs.
Domain and range of $f(x)=\sqrt{2-x}$ ?: Domain: $x\le2$ . Range: $f(x)\ge0$ .
What does $C(n)$ mean?: The value of $C$ (e.g. cost) for the input $n$ (e.g. number of items).
What does an inverse function do?: It reverses (undoes) the effect of $f$ .
Notation for the inverse of $f$ ?: $f^{-1}(x)$ (not $\frac{1}{f(x)}$ ).
How is the graph of $f^{-1}$ related to the graph of $f$ ?: It is the reflection of the graph of $f$ in the line $y=x$ .
Steps to find $f^{-1}(x)$ ?: Write $y=f(x)$ , swap $x$ and $y$ , rearrange for $y$ .
Solving $f(x)=10$ is equivalent to finding what?: $f^{-1}(10)$
Which functions have an inverse?: One-to-one functions: each output comes from only one input.
Domain of $f^{-1}$ ?: The range of $f$ .
Why does $f(x)=x^2$ (all real $x$ ) have no inverse?: It is not one-to-one: $f(-2)=f(2)=4$ .
Find $f^{-1}(x)$ if $f(x)=2x+5$ .: $f^{-1}(x)=\frac{x-5}{2}$

Exam questions on 2.2 Concept of a function, domain, range and inverse

A function is defined by $f(x)=\sqrt{x-3}$ .
Find the value of $x$ for which $f(x)=4$ .2 marks
A taxi company charges a fixed fee of 12 AED plus 2.5 AED for each kilometre travelled. The cost, $C$ AED, of a journey of $n$ km is modelled by $C(n)=12+2.5n$ , for $n\ge0$ .
Find the value of $C^{-1}(100)$ , giving the units of your answer.2 marks
The function $g$ is defined by $g(x)=2x+5$ for $-1\le x\le4$ .
Find the range of $g$ .3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).