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

The required result is
`k(x)=(5^(2x)-1)/(5^x)`

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)=(1)/(x^a)`

`k(x)=5^x-(1)/(5^x)`

Taking LCM,

`k(x)=(5^(2x)-1)/(5^x)`

Therefore, The required result is
`k(x)=(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