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

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]

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