/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 126 If \(f(x)=3 x+7,\) find \(\frac{... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 126

If \(f(x)=3 x+7,\) find \(\frac{f(a+h)-f(a)}{h}\)

Short Answer

Expert verified
The solution to the expression \(\frac{f(a+h)-f(a)}{h}\) for \(f(x) = 3x + 7\) is '3'

Step by step solution

01

Find f(a+h) and f(a)

Substitute \(x = a+h\) into the function to get \(f(a+h) = 3(a+h) + 7\). Then substitute \(x = a\) into the function to get \(f(a) = 3a + 7\).
02

Substitute f(a+h) and f(a) into the expression

Substitute \(f(a+h)\) and \(f(a)\) into the expression \(\frac{f(a+h)-f(a)}{h}\) to get \(\frac{3(a+h)+7 - (3a+7)}{h}\).
03

Simplify the expression

Simplify the expression \(\frac{3(a+h)+7 - (3a+7)}{h}\). The '7's will cancel out and we'll have \(\frac{3h}{h}\). We can then simplify it further by dividing \(3h\) by \(h\) to get final answer as '3'.

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