2 years ago

Write the following expression using a single exponent.

Mathematics

1 answer:

Ymorist [56]2 years ago

5 0

The answer is going to be D

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The difference quotient for the function f(x) is $h+2x-7$

Given :

Difference quotient formula

$\frac{\left(f\left(x+h\right)-f\left(x\right)\right)}{h}$

Given function $f(x) = x^2 - 7x + 8$

find the difference quotient using the formula

first we find out f(x+h) using given f(x)

replace x with x+h

$f(x) = x^2 - 7x + 8 \\f(x+h)=\mathrm{ }\left(x+h\right)^2-7\left(x+h\right)+8\\Expand \; and \; simplify\\f(x+h)=x^2+2xh+h^2-7\left(x+h\right)+8\\f(x+h)=x^2+2xh+h^2-7x-7h+8$

Now replace it in our formula and also replace f(x)

$\frac{\left(f\left(x+h\right)-f\left(x\right)\right)}{h}\\ \frac{x^2+2xh+h^2-7x-7h+8-(x^2 - 7x + 8)}{h} \\\frac{x^2+2xh+h^2-7x-7h+8-x^2 + 7x - 8}{h} \\\\\frac{h^2+2xh-7h}{h}\\factor \; out \; h\\\frac{h\left(h+2x-7\right)}{h}\\h+2x-7$

Learn more :brainly.com/question/23630564

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2 years ago