For all real numbers, f(x)=(x^2+1)/2. If f(a)=25 and f(11)=b, what could be the value of b-a?

I'm confused on how you do these problems. Can someone show me how to do them? Thanks much!

I will start you on b

f(11)=(11^2+1)/2=61 so b is 61

25=(a^2+1)/2 solve for a....

Ok, so f(25)=(25^2+1)/2. 626/2=313. So, a=313. When substituted, 61-313 is -252.

There's a small issue though. This question is multiple, and I don't see a -252 as one of the choices:

a. -14
b. 36
c. 68
d. 77
e. 86

Did I do something wrong?

Shoot I answered this and answer didn't save

To find the value of b-a, we first need to determine the values of a and b separately.

Given that f(x) = (x^2 + 1)/2, we need to substitute the given values of f(a) = 25 and f(11) = b into the equation.

1. Find the value of a:
We know that f(a) = 25, so we can substitute f(x) with 25 and solve for a:
25 = (a^2 + 1)/2

Multiply both sides of the equation by 2 to eliminate the fraction:
50 = a^2 + 1

Subtract 1 from both sides to isolate a^2:
49 = a^2

Take the square root of both sides to find the possible values of a:
a = ±7

Since it asks for the difference b-a, let's find two values of b and calculate the difference for each value.

2. Find the values of b:
We have f(11) = b, so we substitute f(x) with b and x with 11:
b = (11^2 + 1)/2
b = (121 + 1)/2
b = 122/2
b = 61

Therefore, when a = 7, b = 61 and when a = -7, b = 61.

Now we can calculate the difference b-a:
For a = 7: b - a = 61 - 7 = 54
For a = -7: b - a = 61 - (-7) = 61 + 7 = 68

So, b-a can be either 54 or 68, depending on the value of a.