Question

if f(x)=6/(x-2) where x is not equal to 2 and g(x)=kx^2-1, what is the value of k at gf(5)=7?
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Answer 1

Answer:

Answer is in the attachment

Answer 2

SOLUTION

GIVEN

$\displaystyle\sf{f(x) = \frac{6}{x - 2} \: \: where \: x \ne \: 2 }$

g(x) = kx² - 1

TO DETERMINE

The value of k at gf(5) = 7

EVALUATION

Here it is given that

$\displaystyle\sf{f(x) = \frac{6}{x - 2} \: \: where \: x \ne \: 2 }$

Now

$\displaystyle\sf{f(5) = \frac{6}{5 - 2} = \frac{6}{3} = 2 }$

Now it is given that g(x) = kx² - 1

Thus we have g(2) = k × 2² - 1 = 4k - 1

Now by the given condition

gf(5) = 7

$\sf{ \implies \: g(f(5)) = 7}$

$\sf{ \implies \: g(2) = 7}$

$\sf{ \implies \: 4k - 1 = 7}$

$\sf{ \implies \: 4k = 8}$

$\sf{ \implies \: k = 2}$

FINAL ANSWER

Hence the required value of k = 2

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