2.7 Composition of functions
Interactive practice questions
Consider the functions $f\left(x\right)=-2x-3$f(x)=−2x−3 and $g\left(x\right)=-2x-6$g(x)=−2x−6.
Find $f\left(7\right)$f(7).
Hence, or otherwise, evaluate $g\left(f\left(7\right)\right)$g(f(7)).
Now find $g\left(7\right)$g(7).
Hence, evaluate $f\left(g\left(7\right)\right)$f(g(7)).
Is it true that $f\left(g\left(x\right)\right)=g\left(f\left(x\right)\right)$f(g(x))=g(f(x)) for all $x$x?
Yes
No
Consider the functions $f\left(x\right)=-2x+2$f(x)=−2x+2, $g\left(x\right)=4x^2-8$g(x)=4x2−8 and $r\left(x\right)=-3x-8$r(x)=−3x−8.
A conical container is being filled with water, as shown in the diagram. The water is being poured in such a way that the radius of the water's surface increases at a rate of $7$7 cm/s.
Air is being added to a spherical balloon. At a time $t$t (in seconds), the radius $r$r of the balloon (in cm) can be given by the function $r\left(t\right)=3\sqrt{t}$r(t)=3√t. The volume of a sphere in terms of its radius is given by the formula $V\left(r\right)=\frac{4}{3}\pi r^3$V(r)=43πr3.