Graph f(x)=2^x+1 and g(x)=−x+4 on the same coordinate plane. What is the solution to the equation f(x)=g(x) ?x =

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