Question

find the indicated function values for the function g(x) = 2x - 1.
a. g(0) b. g(2) c. g\left(\frac{3}{2}\
ight) d. g(5b) e. g(b + 7)

a. g(0) = -1 (simplify your answer.)
b. g(2) = 3 (simplify your answer.)
c. g\left(\frac{3}{2}\
ight) = 2 (simplify your answer.)
d. g(5b) = 10b - 1 (simplify your answer.)
e. g(b + 7) = \square (simplify your answer.)

Explanation:

Step1: Substitute \( x = b + 7 \) into \( g(x) \)

We know that \( g(x)=2x - 1 \), so when \( x=b + 7 \), we substitute it into the function: \( g(b + 7)=2(b + 7)-1 \)

Step2: Distribute the 2

Using the distributive property \( a(b + c)=ab+ac \), we get \( 2(b + 7)=2b+14 \), so the function becomes \( g(b + 7)=2b + 14-1 \)

Step3: Simplify the constant terms

Subtract 1 from 14: \( 14-1 = 13 \), so \( g(b + 7)=2b+13 \)

Answer:

\( 2b + 13 \)