CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let f(x) = 2x + 3 and g(x) = (x − 3)/2 on the real numbers. Let h(x) = f(g(x)) + g(f(x)) + f(1). What is the value of h(4)?
The value of h(4) is 13. Since f and g are inverse functions, f(g(4)) and g(f(4)) each equal 4, giving 8, and f(1) = 2(1) + 3 = 5 is added to give 13.
- A13Correct
- B9
- C4
- D17
Explanation
f and g are inverses of each other, so f(g(x)) = x and g(f(x)) = x. Then h(4) = 4 + 4 + f(1) = 8 + 5 = 13. Dropping f(1) gives 8, and using f(1) = 1 gives 9, both wrong.
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