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irinina [24]
3 years ago
11

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

Mathematics
1 answer:
rewona [7]3 years ago
6 0

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}

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