Suppose f(x)= sqrt x^2+6x+10 and g(x)=9x+8
f(g(x))=
f(g(-5))=
To find f(g(x)), substitute g(x) into f(x).
f(g(x)) = sqrt((g(x))^2 + 6(g(x)) + 10)
Now let's substitute g(x) = 9x + 8 into f(g(x)):
f(g(x)) = sqrt((9x + 8)^2 + 6(9x + 8) + 10)
To find f(g(-5)), substitute x = -5 into f(g(x)):
f(g(-5)) = sqrt((9(-5) + 8)^2 + 6(9(-5) + 8) + 10)
Simplifying the expression inside the square root:
f(g(-5)) = sqrt((-45 + 8)^2 + 6(-45 + 8) + 10)
f(g(-5)) = sqrt((-37)^2 + 6(-37) + 10)
Calculating:
f(g(-5)) = sqrt(1369 - 222 + 10)
f(g(-5)) = sqrt(1157)
To find f(g(x)), we will substitute g(x) into f(x):
f(g(x)) = sqrt((g(x))^2 + 6(g(x)) + 10)
To find f(g(-5)), we will substitute g(-5) into f(x):
f(g(-5)) = sqrt((g(-5))^2 + 6(g(-5)) + 10)
Now let's solve these equations step by step.
1. f(g(x)):
f(g(x)) = sqrt((g(x))^2 + 6(g(x)) + 10)
Since g(x) = 9x + 8, we can substitute it into the equation:
f(g(x)) = sqrt((9x + 8)^2 + 6(9x + 8) + 10)
Expanding and simplifying:
f(g(x)) = sqrt(81x^2 + 144x + 64 + 54x + 48 + 10)
f(g(x)) = sqrt(81x^2 + 198x + 122)
2. f(g(-5)):
f(g(-5)) = sqrt((g(-5))^2 + 6(g(-5)) + 10)
Since g(-5) = 9(-5) + 8 = -45 + 8 = -37, we can substitute it into the equation:
f(g(-5)) = sqrt((-37)^2 + 6(-37) + 10)
Expanding and simplifying:
f(g(-5)) = sqrt(1369 - 222 + 10)
f(g(-5)) = sqrt(1157)
To find the value of f(g(x)), we need to substitute the expression for g(x) inside the function f(x).
Given that f(x) = sqrt(x^2 + 6x + 10) and g(x) = 9x + 8, we substitute g(x) into f(x) as follows:
f(g(x)) = f(9x + 8)
Similarly, to find f(g(-5)), we substitute g(-5) into f(x):
f(g(-5)) = f(9(-5) + 8)
Now we can simplify these expressions to find the respective values.