Mathematics 0580: FUNCTIONS Topical Past Paper Questions

**(a)** $f(x) = 3x + 1 \qquad g(x) = 5 - 3x$ > **(i)** Find $x$ when $f(x) = g(x)$. [2] > **(ii)** Find $g^{-1}(x)$. [2] > **(iii)** Find $\mathrm{gg}(x)$. > > Give your answer in its simplest form. [2] **(b)** $\mathrm{h}(x) = 2^{2x}$ > Find $x$ when $\mathrm{h}^{-1}(x) = 2$. [2…

$f(x) = 5^x \quad g(x) = 3x - 2 \quad h(x) = x^2 + 1$ **(a)** Find $f(5)$. [1] **(b)** Find $g(8x)$. [1] **(c)** Find $g^{-1}(x)$. $g^{-1}(x) =$ [2] **(d)** Find the positive solution of $gh(x) = 364$. $x =$ [3] **(e)** Find $ff^{-1}(12)$. [1]

$f(x) = \frac{1}{x}, x \neq 0 \quad g(x) = 3x - 5 \quad h(x) = 2^x$ (a) Find. > (i) $gf(2)$ [2] > > (ii) $g^{-1}(x)$ > $g^{-1}(x) =$ [2] (b) Find in its simplest form $g(x-2).$ [2] (c) Find the value of $x$ when > (i) $fg(x) = 0.1$ > $x =$ [2] > > (ii) $h(x) - g(7) = 0.$ > $x =$…