Composite and inverse functions can be determined for trigonometric, logarithmic, exponential or algebraic functions.

What does \({x^2} + 4x - 5\) expressed in the form \({(x + a)^2} + b\) equal?

\[{(x + 2)^2} - 5\]

\[{(x + 2)^2} - 9\]

\[{(x + 4)^2} - 20\]

What could the graph below represent?

\[y = 1 + 2\sin x^\circ\]

\[y = 1 + \sin 2x^\circ\]

\[y = \sin (2x + 1)\]

If \(h(x) = {x^3}\) and \(f(x) = \cos 2x\), what is \(f(h(x))\) equal to?

\[\cos 2{x^3}\]

\[{\cos ^3}2x\]

\[{\cos ^3}8{x^3}\]

If \(f(x) = 3{x^2}\) and \(g(x) = x - 4\), what is \(g(f(x))\) equal to?

\[9{x^2} - 4\]

\[3{x^2} - 4\]

\[3{(x - 4)^2}\]

Functions 'g' and 'h' are defined by \(g(x) = \frac{1}{x}\) and h(x) = 8 - 5x where \(x \in R\). What does \(h(g(x))\) equal?

\[\frac{1}{{8 - 5x}}\]

\[\frac{3}{x}\]

\[\frac{{8x - 5}}{x}\]

When \(2{x^2} + 8x - 3\) is written in the form \(a{(x + b)^2} + c\), what are the values of 'a', 'b' and 'c'?

\[a = 2,\,b = 2,\,c = - 11\]

\[a = 2,\,b = 2,\,c = - 7\]

\[a = 2,\,b = 2,\,c = - 3\]

What is \(9 - 4x - {x^2}\) expressed in the form \(9 - {(x + q)^2}\) equal to?

\[5 - {(x - 2)^2}\]

\[13 - {(x + 2)^2}\]

\[13 - {(x - 2)^2}\]