## Exam-Style Question on Functions## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 408. This question is similar to one that appeared on an A-Level paper. The use of a calculator is allowed.

The functions \(f\) and \(g\) are defined as:

$$ f(x) = \sqrt{3x+4} \text{ for } x \ge -1 $$ $$ g(x) = x^2 - 3x \text{ for all real values of }x $$(a) Find \( f^{-1}(x) \)

(b) State the domain of \( f^{-1}\).

(c) Find the range of \(g\).

(d) Find \(gf(x)\).

(e) Solve the equation \(gf(x) = 10\).

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