If f(x) and g(x) are inverse…

Maths Questions

If f(x) and g(x) are inverse functions of each other, which of the following graphs represents f(g(x))?

Answer

The attached graph represents f(x) = x. Explanation: Inverse functions yield the composite function f(g(x)) equating to f(x) = x. For instance, consider f(x) = 2x – 4, rewritten as y = 2x – 4. To determine its inverse, we rearrange to isolate x: adding 4 gives y + 4 = 2x, then dividing both sides by 2 results in (y + 4)/2 = x, simplifying to y/2 + 2 = x. By swapping x and y, we find the inverse as y = 1/2x + 2, designated as g(x). Calculating the composite function f(g(x)), we have f(1/2x + 2) = 2(1/2x + 2) – 4, which simplifies to x. Thus, the function’s composite confirms the graph with a slope of 1 and a y-intercept of 0.

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