Given f(x)= 2^x +1
g(x)= -x +4
We have to find the value of x which satisfy the condetion : f(x)= g(x)
Solution : let us place expression given for f(x) and g(x) equal to each other
This gives us : 2^x + 1 = -x+ 4
Let us bring all x terms on left side only
we add x on both sides this makes : 2^x +1 +x = -x+ 4 +x
on the right side -x and +x becomes a "0"
we get : 2^x + 1 + x = 4
* let us nopw bring all the numeric terms on left side only
subtract 1 from both sides : 2^x + 1 + x - 1 = 4- 1
on the left side +1 and -1 becomes a "0"
on the rigth side 4-1 becomes a "3"
equation look like : 2^x + x = 3
We can see the right side is an odd number
on the left side there is sum of two terms one of them is 2^x which is an even number always .
we know that sum of an even number with an even number result out an even number
but we want a result as an odd number (3)
this suggest that x should be an odd number .
Also the sum of 2^x and x is 3 so 2^x should be smaller than 3
the smallest value ( x being an integer )
2^x can have is : 2^1= 2 which is for x=1
let us check plugging x= 1 . 2^1 + 1 = 3 which is TRUE
Hence answer is x= 1
