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

Step-by-step explanation:

Given : You have two exponential functions. One function has the formula $g(x) = 5 ^x$ . The other function has the formula $h(x) = 5^{-x}$ .

To find : Which gives formula for  $k(x)=(g-h)(x)$?

Solution :

Let $g(x) = 5 ^x$ ....(1)

$h(x) = 5^{-x}$ .....(2)

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

We can write it as,

$k(x)=g(x)-h(x)$ ......(3)

Now, substitute the values from (1) and (2) in equation (3),

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

Open the parenthesis on right hand side of equation, we get

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

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

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

Taking LCM,

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

Therefore, The required result is  $k(x)=\frac{5^{2x}-1}{5^x}$

Answer 2

We are given with two functions here: h(x) is 5^-x and g(x) is 5^x . we are asked in the problem to determine the value of the expression (g-h)(x). In this case, we just have to employ subtraction to the given functions. That is 

(g-h)(x) = 5^x - 5^-x
             = 5^x -1/5^x
             = (5^2x -1)/5^x