in problems 79 - 90, find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, $h\neq0$…

in problems 79 - 90, find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, $h\neq0$, for each function. be sure to simplify.\n79. $f(x)=4x + 3$\n80. $f(x)=-3x + 1$\n81. $f(x)=x^{2}-4$\n82. $f(x)=3x^{2}+2$\n83. $f(x)=x^{2}-x + 4$\n84. $f(x)=3x^{2}-2x + 6$\n85. $f(x)=\frac{1}{x^{2}}$\n86. $f(x)=\frac{1}{x + 3}$\n87. $f(x)=\frac{2x}{x + 3}$\n88. $f(x)=\frac{5x}{x - 4}$\n89. $f(x)=sqrt{x - 2}$ hint: rationalize the numerator.\n90. $f(x)=sqrt{x + 1}$
Answer
Explanation:
Step1: Encontrar (f(x + h)) para (f(x)=4x + 3)
Sustituir (x) por (x + h) en (f(x)): (f(x + h)=4(x + h)+3=4x+4h + 3)
Step2: Calcular la diferencia cuociente
(\frac{f(x + h)-f(x)}{h}=\frac{(4x + 4h+3)-(4x + 3)}{h})
Step3: Simplificar la expresión
(\frac{4x + 4h+3 - 4x - 3}{h}=\frac{4h}{h}=4)
Answer:
4