Functions f and g are defined for x by i. Find and simplify expressions for

Question:

Functions f and g are defined for x ∈ ℝ by

i. Find and simplify expressions for fg(x) and gf(x).

ii. Hence find the value of a for which fg(a) = gf(a).

iii. Find the value of b (b ≠ a) for which g(b) = b.

iv. Find and simplify an expression for f⁻¹g(x). The function h is defined by h : x ↦ x² − 2, for x ≤ 0.

v. Find an expression for h⁻¹(x).

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Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

ISBN: 9781108407144

1st Edition

Authors: Sue Pemberton, Julian Gilbey

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Question Posted: Mar 09, 2023 05:43 AM

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Functions f and g are defined for x by i. Find and simplify expressions for

Question:

f: x + 2x + 1, g : x + x² -2.

Step by Step Answer:

i To find fgx we substitute gx x2 2 into fx 2x 1 fgx fgx fx2 2 2x2 2 1 2x2 3 To find gfx ...View the full answer

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

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