If f(x) = 2x - 3 and g(x) = 5x + 7, which of the following defines f(g(x))?

Rationale

f(g(x)) = 10x - 8.

To find f(g(x)), we first substitute g(x) into the function f(x). Calculating f(g(x)) involves substituting 5x + 7 into the expression for f(x), leading to the simplified form of 10x - 8.

A (10x+1) YOUR ANSWER

This choice suggests that when substituting g(x) into f(x), the output somehow results in a linear function with a positive constant. However, the correct computation shows that the constant from the substitution leads to a negative value, making this option incorrect.

B (10x-8) CORRECT

This option correctly represents the outcome of the composition of functions. By substituting g(x) = 5x + 7 into f(x) = 2x - 3, we calculate f(g(x)) = 2(5x + 7) - 3, which simplifies to 10x - 14 - 3 = 10x - 8.

C (10x+21) YOUR ANSWER

This choice incorrectly indicates that the process of function composition results in a positive constant. The calculation of f(g(x)) does not yield this outcome, as the constants from the substitution lead to a subtraction rather than an addition.

D (10x-21) YOUR ANSWER

This option implies a greater negative adjustment than what actually results from the correct substitution. The calculations yield a final constant of -8, not -21, demonstrating that this choice is not supported by the correct function composition.

Conclusion

The composition of functions f(g(x)) results in 10x - 8, derived from the substitution of g(x) into f(x). Each of the incorrect options overlooks the proper arithmetic performed during the function composition, which is essential for accurately determining the resultant expression. Understanding function composition is crucial in algebra, making it a valuable skill for solving complex problems.

If f(x) = 2x - 3 and g(x) = 5x + 7, which of the following defines f(g(x))?

f(g(x)) = 10x - 8.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test