Find (fog)(2)
f(x)=Squareroot 4-x; g(x)=1-3x^2
Find (gof)(-2) for the same problem.
(fog)2 = f(f(2))
g(2) = 1 - 12 = -11
f(g(2) = f(-11) = √(4 -(-11)) = √15
do the second one in the same way
To find (fog)(2), we need to substitute the value of 2 into the function g first, and then substitute the resulting value into the function f.
1. Start with the function g(x): g(x) = 1 - 3x^2.
2. Substitute x = 2 into the function g(x): g(2) = 1 - 3(2)^2.
3. Simplify the equation: g(2) = 1 - 3(4).
g(2) = 1 - 12.
g(2) = -11.
Now that we have the value of g(2), we can substitute it into the function f(x) to find (fog)(2).
1. Start with the function f(x): f(x) = √(4 - x).
2. Substitute x = -11 into the function f(x): f(-11) = √(4 - (-11)).
3. Simplify the equation: f(-11) = √(4 + 11).
f(-11) = √15.
Therefore, (fog)(2) = √15.
To find (gof)(-2), we need to substitute the value of -2 into the function f first, and then substitute the resulting value into the function g.
1. Start with the function f(x): f(x) = √(4 - x).
2. Substitute x = -2 into the function f(x): f(-2) = √(4 - (-2)).
3. Simplify the equation: f(-2) = √(4 + 2).
f(-2) = √6.
Now that we have the value of f(-2), we can substitute it into the function g(x) to find (gof)(-2).
1. Start with the function g(x): g(x) = 1 - 3x^2.
2. Substitute x = √6 into the function g(x): g(√6) = 1 - 3(√6)^2.
3. Simplify the equation: g(√6) = 1 - 3(6).
g(√6) = 1 - 18.
g(√6) = -17.
Therefore, (gof)(-2) = -17.