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Question

If f(x)=3x+82xAf(x)=\frac{3 x+8}{2 x-A} and f(0)=2f(0) = 2, what is the value of A?

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f(x)=3x+82xAf(x)=\dfrac{3x+8}{2x-A}

Substitute 00 for xx in the equation for ff

f(0)=3(0)+82(0)Af(0)=\dfrac{3(0)+8}{2(0)-A}

f(0)=8Af(0)=-\dfrac{8}{A}

It is given that f(0)=2f(0)=2, so we can write

2=8A2=-\dfrac{8}{A}

Divide both sides by 2

1=4A1=-\dfrac{4}{A}

Multiply both sides by AA

A=4A=-4

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