Functions, Graphs & Logarithms

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Exam-level questions worked step by step. Try each one yourself first — then expand the solution and compare routes.

Q1.

Find the value of $\log_2 32 + \log_3 27$ .

Q2.

If $f(x) = \dfrac{2x+3}{x-1}$ , then $f^{-1}(5)$ equals:

Q3.

The minimum value of $f(x) = x^2 - 12x + 40$ is:

Q4.

The minimum value of $|x - 1| + |x - 7|$ for real $x$ is:

Q5.

If $\log_2 x + \log_2 (x - 7) = 3$ , then $x$ equals: