Question

You have two exponential functions. One function has the formula g(x) = 5 x . The other function has the formula h(x) = 5-x . Which option below gives formula for k(x) = (g - h)(x)?

Answer 1

Answer:

The value of $k(x)=\frac{5^{2x}-1}{5^x}$

Step-by-step explanation:

We have given two function $g(x)=5^x\text{and}h(x)=5^{-x}$

We have to find k(x)=(g-h)(x)

$k(x)=g(x)-h(x)$           (1)

We will substitute the values in equation (1) we will get

$k(x)=5^x-(5^{-x})$

Now, open the parenthesis on right hand side of equation we will get

$k(x)=5^x-5^{-x}$

Using $x^{-a}=\frac{1}{x^a}$

$k(x)=5^x-\frac{1}{5^x}$

Now, taking LCM which is $5^x$ we will get after simplification

$k(x)=\frac{5^{2x}-1}{5^x}$

Hence, the value of $k(x)=\frac{5^{2x}-1}{5^x}$

Answer 2

Given the exponential functions $g(x)= 5^{x}$ and $h(x)= 5^{-x}$

$k(x)=(g-h)(x)$
$k(x)=g(x)-h(x)$
$k(x)= 5^{x} - 5^{-x}$
$k(x)= 5^{x} - \frac{1}{ 5^{x} }$
$k(x)= \frac{ 5^{x} 5^{x} }{ 5^{x} } - \frac{1}{ 5^{x} }$
$k(x)= \frac{ 5^{2x} }{ 5^{x} } - \frac{1}{ 5^{x} }$
$k(x)= \frac{ 5^{2x}-1 }{ 5^{x} }$