Question 31

f(g(x)) is defined as 10x - 8.

To find f(g(x)), we first substitute g(x) into f(x). This results in f(5x + 7), which simplifies to 2(5x + 7) - 3, ultimately yielding 10x - 8.

A) 10x + 1

Option A is incorrect because it suggests that the result of f(g(x)) is 10x + 1, which does not align with the calculations made. The correct expression derived from substituting g(x) into f(x) does not yield this outcome.

B) 10x - 8

Option B is the correct answer. By substituting g(x) into f(x), we find f(g(x)) = f(5x + 7) = 2(5x + 7) - 3, which simplifies to 10x - 8. This matches the derived expression perfectly.

C) 10x + 21

Option C is incorrect because it suggests that after substituting g(x) into f(x), the resulting expression would yield 10x + 21. However, the calculations show that the correct simplification leads to 10x - 8, not this option.

D) 10x - 21

Option D is also incorrect. While it presents a similar structure to the correct answer, it inaccurately reflects the outcome of the substitution process. The arithmetic performed clearly indicates that the result is 10x - 8, not 10x - 21.

Conclusion

The correct answer, 10x - 8, is definitively derived from the function composition of f and g as demonstrated through substitution. All other options fail to match the result of the calculations, confirming that they are not valid representations of f(g(x)).