1 of 8 0-day streak

Form and analyse composite functions

Question 1 of 8

No calculator

Use the stated domains; find component ranges from the displayed rules when needed

function	rule	stated domain
\(f\)	\(-\frac{2}{3}x-2\)	\(\left[-9,9\right]\)
\(g\)	\(-\frac{1}{22}(x-1)^2+1\)	\(\left[-9,9\right]\)

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)3 marks

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

Enter the coefficients in the form \(h(x)=Ax^2+Bx+C\)

\(A\) \(B\) \(C\)

(b)1 mark

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

\left[-9,11\right)

\left[-9,13\right)

\left[-9,12\right)

\left[-9,9\right]

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

Enter the coefficients in the form \(h(x)=Ax^2+Bx+C\)

\(A\) \(B\) \(C\)

(d)1 mark

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

\left[-9,11\right)

\left[-9,13\right)

\left[-9,9\right]

\left[-9,12\right)