Question

Functions f and A are defined by these equations:f(x = 80 - 15xA(x = 25 + 10xWhich function has a greater value when xis 2.5, a(x) or f(x)?

Answer 1

To compare the values of the functions \( f(x) \) and \( A(x) \) at \( x = 2.5 \), we first need to evaluate each function using the given definitions.

1. **Evaluate \( f(x) \)**:
\[
f(x) = 80 - 15x
\]
Substitute \( x = 2.5 \):
\[
f(2.5) = 80 - 15(2.5) = 80 - 37.5 = 42.5
\]

2. **Evaluate \( A(x) \)**:
\[
A(x) = 25 + 10x
\]
Substitute \( x = 2.5 \):
\[
A(2.5) = 25 + 10(2.5) = 25 + 25 = 50
\]

Now, we can compare the values:
- \( f(2.5) = 42.5 \)
- \( A(2.5) = 50 \)

Since \( 50 > 42.5 \), the function \( A(x) \) has a greater value than \( f(x) \) when \( x = 2.5 \).