Question

if f(x) = 5^x , Then prove that f(x+1) - f(x) = 4f(x)​

Answer 1

It is proven that if f(x) = 5ˣ, then f(x+1) - f(x) = 4f(x)​

Given:

f(x) = 5ˣ

To find:

Prove that f(x+1) - f(x) = 4f(x)​

Solution:

Given that f(x) = 5ˣ  

Now find f(x+1) - f(x) and 4f(x) to prove given statement

To find f(x+1) take x = (x+1) and sustitute in given function

=> f(x) = f(x+1)  

=> f(x+1) = 5^(x+1) = 5ˣ + 5¹    

=> f(x+1) = 5ˣ ( 5)        

From the above calculation,

=> f(x+1) - f(x) = 5ˣ (5) - 5ˣ  

=> f(x+1) - f(x) = 5ˣ [ 5 - 1]  

=> f(x+1) - f(x) = 4(5ˣ) -----(1)

Now find 4f(x)​

=> 4f(x)​ = 4(5ˣ) ----(2)  

From (1) and (2)

=> f(x+1) - f(x) = 4(5ˣ) = 4f(x)​  

Therefore,

It is proven that if f(x) = 5ˣ, then f(x+1) - f(x) = 4f(x)​

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