Question

For function of g,g(0)=1 and g(1)=5 assuming g is a linear function what is g(3)
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Answer 1

`g(3) = 13`

Explanation:

Given

`g(0) = 1`

`g(1) = 5`

Required

Find g(3)

Since g(x) is a linear function, then:

`g(x) = mx + c`

For:
`g(0) = 1`

`g(x) = mx + c`

`g(0) = m*0 + c`

`1 = 0 + c`

`1 = c`

`c = 1`

For:
`g(1) = 5`

`g(x) = mx + c`

`g(1) = m * 1 + c`

`5 = m * 1 + c`

`5 = m + c`

Substitute
`c = 1`

`5 = m + 1`

`m = 5 - 1`

`m =4`

So, the function is:

`g(x) = mx + c`

`g(x) = 4x + 1`

Calculate g(3)

`g(3) = 4*3 + 1`

`g(3) = 12 + 1`

`g(3) = 13`