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1 of 8 0-day streak

Form and analyse composite functions

DIFFICULTYintrostandardchallengeexam
Question 1 of 8

No calculator

Form the composite in the stated order, then check its allowed inputs and outputs

functionrulestated domain
\(f\)\(\frac{2}{3}x-1\)\(\left[-8,8\right]\)
\(g\)\(\frac{1}{3}x+2\)\(\left[-8,8\right]\)

The first row defines \(f\) and the second row defines \(g\). Use the stated domain in each row; do not extend a function beyond that domain

\[\operatorname{Ran}(f)\text{ and }\operatorname{Ran}(g)\text{ must be found from the displayed rules and domains when needed.}\]
(a)2 marks

Find the rule for \((f\circg)(x)\)

Enter the coefficients in the form \(h(x)=Ax+B\)

(b)1 mark

Select the domain of \((f\circg)(x)\) from the exact set choices

(c)2 marks

Find the rule for \((g\circf)(x)\)

Enter the coefficients in the form \(h(x)=Ax+B\)

(d)1 mark

Select the domain of \((g\circf)(x)\) from the exact set choices