Create a Function

A linear function is given:
a(x) = 26 - 12.4x
​
The function b is also linear. The equation a(x) = b(x) has exactly one solution at x = 5.
Create a possible equation for function b.

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Substitute 5, in for x, into a(x) = 26 - 12.4x

a(5) = 26 - 12.4(5) {substituted 5 for x}
= 26 - 62 {multiplied}
= -36 {subtracted}

When 5 is substituted for x, into a(x), the result is -36.

Therefore, creating any function b(x), where the (5,-36) is a solution would suffice.

-36x
——- = b(x) {created an equation where (5,-36) will be a solution}
5

If 5 is substituted in for x, into b(x), the result is -36.

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