Suppose f(x)= sqrt x^2+3x+9 and g(x)=10x-9
f(g(x))=
f(g(-5))=
To evaluate f(g(x)), we need to substitute g(x) into f(x).
f(x) = √(x^2 + 3x + 9)
g(x) = 10x - 9
Replacing x in f(x) with g(x):
f(g(x)) = √((10x - 9)^2 + 3(10x - 9) + 9)
To evaluate f(g(-5)), we substitute -5 into g(x):
g(-5) = 10(-5) - 9
= -50 - 9
= -59
f(g(-5)) = √((-59)^2 + 3(-59) + 9)
Now we can calculate f(g(-5)) by substituting -59 into f(x):
f(g(-5)) = √((-59)^2 + 3(-59) + 9)
= √(3481 - 177 + 9)
= √(3304)
≈ 57.42
To find f(g(x)), start by substituting g(x) into f(x):
f(g(x)) = sqrt((g(x))^2 + 3(g(x)) + 9)
Now substitute g(x) with its expression:
f(g(x)) = sqrt((10x - 9)^2 + 3(10x - 9) + 9)
Now simplify the expression:
f(g(x)) = sqrt((100x^2 - 180x + 81) + (30x - 27) + 9)
= sqrt(100x^2 - 150x + 63)
To find f(g(-5)), substitute x = -5 into the expression:
f(g(-5)) = sqrt(100(-5)^2 - 150(-5) + 63)
= sqrt(2500 + 750 + 63)
= sqrt(3313)
Therefore, f(g(-5)) = sqrt(3313), which is approximately equal to 57.54 (rounded to two decimal places).
To find f(g(x)), we first need to substitute g(x) into the function f(x). So, we replace every occurrence of x in f(x) with g(x) and simplify.
f(g(x)) = sqrt((g(x))^2 + 3(g(x)) + 9)
Now, let's substitute g(x) = 10x - 9 into f(x).
f(g(x)) = sqrt((10x - 9)^2 + 3(10x - 9) + 9)
Now, we simplify the expression inside the square root.
f(g(x)) = sqrt(100x^2 - 180x + 81 + 30x - 27 + 9)
Combining like terms, we have:
f(g(x)) = sqrt(100x^2 - 150x + 63)
So, f(g(x)) = sqrt(100x^2 - 150x + 63).
Now, let's calculate f(g(-5)) by substituting x = -5 into f(g(x)).
f(g(-5)) = sqrt(100(-5)^2 - 150(-5) + 63)
Simplifying further:
f(g(-5)) = sqrt(100(25) + 750 + 63)
f(g(-5)) = sqrt(2500 + 750 + 63)
f(g(-5)) = sqrt(3313)
Therefore, f(g(-5)) equals the square root of 3313.