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Find f(x) if f is a linear function that has given properties. f(-1)=1, f(3)=9 f(x)=

Find f(x) if f is a linear function that has given properties.

f(-1)=1, f(3)=9

f(x)=

Solutions

Expert Solution

Given is a linear function where and

We know any linear function has to be of the form:

-----(1)

where a is the coefficient of x and b is a constant

f(-1) and f(3) are obtained by substituting x=-1 and x=3 in (1) respectively.

Substituting x=-1 in (1):

-----(2)

Substituting x=3 in (1):

-------(3)

Rewriting (3) to obtain the value of b:

-----(4)

Substitute (4) in the place of "b" in (2)

------(5)

Sunstitute (5) in (4)

Since

-----(6)
Substituting (5) and (6) in (1)

So, the linear function is f(x)=2x+3

milcah answered 1 year ago

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