Mathematics 0580 · IGCSE · Functions

Functions — practice question

The functions are $f(x) = (3x + 1)(x + 5)(x - 4)$, $g(x) = 2x - 3$, and $h(x) = 4^{2x - 1}$.
(a(i))[1]

Determine $f(0)$.

(a(ii))[2]

Determine $g^{-1}(x)$.

(a(iii))[2]

Find $gh(2)$.

(b)[2]

Given that $g(2x) = 7$, find the value of $x$.

(c)[3]

Simplify the expression $g(x^2) + g g(x) + 1$.

(d)[2]

Determine $h^{-1}(16)$.

(e)[3]

The function $f(x) = (3x + 1)(x + 5)(x - 4)$ can be expressed as $f(x) = ax^3 + bx^2 + cx + d$. Determine the values of $a$, $b$, $c$ and $d$.

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