Question 53

f(g(x)) is represented by 2x² - 2.

To find f(g(x)), we need to substitute g(x) into f(x). Thus, f(g(x)) = f(x² - 3) = 2(x² - 3) + 1 = 2x² - 6 + 1 = 2x² - 5.

A) 2x² - 2

This option states that f(g(x)) is equal to 2x² - 2. However, upon substituting g(x) into f(x), we find that f(g(x)) simplifies to 2x² - 5, making this option incorrect.

B) 2x² + 1

This option suggests that f(g(x)) equals 2x² + 1. Evaluating f(g(x)) leads to 2(x² - 3) + 1 = 2x² - 6 + 1 = 2x² - 5, which does not match this option, thus it's incorrect.

C) 2x² - 5

This option correctly represents f(g(x)) as it is derived from substituting g(x) into f(x). The calculation shows that f(g(x)) = 2(x² - 3) + 1 = 2x² - 5.

D) 2x² - 3

This option claims that f(g(x)) equals 2x² - 3. However, substituting g(x) into f(x) yields 2x² - 5, not 2x² - 3, rendering this option incorrect.

Conclusion

The correct answer is C) 2x² - 5, which accurately represents the function f(g(x)) after proper substitution. Options A, B, and D do not match the derived expression from the calculations and therefore are not valid representations of f(g(x)).