Mathematics 9709 · AS & A Level · Functions

Functions — practice question

(a)[2]

Express $3x^2 - 12x + 14$ in the form $3(x+a)^2 + b$, with $a$ and $b$ as the constants to determine.

(b)[1]

The function $f(x) = 3x^2 - 12x + 14$ is defined for $x \ge k$, where $k$ is constant. Determine the least value of $k$ for which $f^{-1}$ exists.

(c)[3]

For the remainder of this question, assume that $k$ takes the value found in part (b). Find an expression for $f^{-1}(x)$.

(d)[3]

Hence or otherwise, solve the equation $ff(x) = 29$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Writing $3(x-2)^2+2$ for the function, or giving $a=-2$, $b=2$.

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