Answer:
[tex]g(3) = 13[/tex]
Step-by-step explanation:
Given
[tex]g(0) = 1[/tex]
[tex]g(1) = 5[/tex]
Required
Find g(3)
Since g(x) is a linear function, then:
[tex]g(x) = mx + c[/tex]
For: [tex]g(0) = 1[/tex]
[tex]g(x) = mx + c[/tex]
[tex]g(0) = m*0 + c[/tex]
[tex]1 = 0 + c[/tex]
[tex]1 = c[/tex]
[tex]c = 1[/tex]
For: [tex]g(1) = 5[/tex]
[tex]g(x) = mx + c[/tex]
[tex]g(1) = m * 1 + c[/tex]
[tex]5 = m * 1 + c[/tex]
[tex]5 = m + c[/tex]
Substitute [tex]c = 1[/tex]
[tex]5 = m + 1[/tex]
[tex]m = 5 - 1[/tex]
[tex]m =4[/tex]
So, the function is:
[tex]g(x) = mx + c[/tex]
[tex]g(x) = 4x + 1[/tex]
Calculate g(3)
[tex]g(3) = 4*3 + 1[/tex]
[tex]g(3) = 12 + 1[/tex]
[tex]g(3) = 13[/tex]
