Question

Let f(x) = (5)^x+1 .Evaluate f (-3) without using a calculator

Answer 1

Answer:

$f\left(-3\right)=\frac{126}{125}$

Step-by-step explanation:

Given

$f\left(x\right)\:=\:\left(5\right)^x+1$

Putting x = -3 to find f(-3)

$f\left(-3\right)\:=\:\left(5\right)^{\left(-3\right)}+1$

as

$5^{-3}=\frac{1}{125}$       ∵  $\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

so

$f\left(-3\right)=\frac{1}{125}+1$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot \:125}{125}$

$f\left(-3\right)=\frac{1\cdot \:\:125}{125}+\frac{1}{125}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$f\left(-3\right)=\frac{1\cdot \:\:125+1}{125}$

$f\left(-3\right)=\frac{126}{125}$      ∵ $1\cdot \:125+1=126$

Thus,

$f\left(-3\right)=\frac{126}{125}$