Karen Morrison and Nick Hamshaw Solutions for Exercise 9: Examination practice

Make $y$ the subject of the formula.

$A={\mathrm{\pi x}}^2-{\mathrm{\pi y}}^2$

$f\left(x\right)=5x-2$, $g\left(x\right)=\frac{7}{x-3}, x\ne 3$, $h\left(x\right)=2x^2+7x$.

Solve $g\left(x\right)=x+3$.

$f\left(x\right)=5x-2$, $g\left(x\right)=\frac{7}{x-3}, x\ne 3$, $h\left(x\right)=2x^2+7x$.

Find $fh\left(x\right)=11$, showing all your working and giving your answers correct to $2$ decimal places.

If $f\left(x\right)=5x-2$. Find $f^{-1}\left(x\right)$.

$f\left(x\right)=5x-2$, $g\left(x\right)=\frac{7}{x-3}, x\ne 3$, $h\left(x\right)=2x^2+7x$.

Solve $g^{-1}\left(x\right)=-0.5$

$f\left(x\right)=2x+5$, $g\left(x\right)=2^x$, $h\left(x\right)=7-2x$

Find $f^{-1}\left(x\right)$.

$f\left(x\right)=2x+5$, $g\left(x\right)=2^x$, $h\left(x\right)=7-2x$

$f\left(x\right)=2x+5$, $g\left(x\right)=2^x$, $h\left(x\right)=7-2x$

Find the integer values of $x$ which satisfy this inequality:

$1<f\left(x\right)\le 9$