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Graph of f(x)
Answer the following.
Find the value of such that .
Find the value of $x$ such that $g^{-1}(x) = h^{-1}(x)$.
Answer
Answer
AISetting $g^{-1}(x) = h^{-1}(x)$:
$(3 - \sqrt{x + 8})^2 = (3 + \sqrt{x + 8})^2$
$9 - 6\sqrt{x + 8} + x + 8 = 9 + 6\sqrt{x + 8} + x + 8$
$-6\sqrt{x + 8} = 6\sqrt{x + 8} \Rightarrow 12\sqrt{x + 8} = 0 \Rightarrow \sqrt{x + 8} = 0 \Rightarrow x + 8 = 0 \Rightarrow x = -8$.
Final answer: -8
From ISC 2027 Specimen Mathematics Paper 1, question 16(v).