The value of f(g(−3)) is 1/10.
We are tasked with finding the value of f(g(−3)), where g(x)=(x−1)^2 and f(x)= 2/x+4.
Evaluate g(−3):
Start by substituting −3 into the function g(x):
g(−3)=(−3−1)^2 =(−4)^2 =16.
Substitute g(−3) into f(x):
With the value of g(−3) now known, substitute it into the function f(x):
f(g(−3))=f(16)= 2/16+4.
Simplify the expression:
Combine the terms in the denominator: 2/20.
Reduce to the simplest form:
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2: 1/10.
Final Result:
Therefore, f(g(−3)) simplifies to 1/10, which is equivalent to 0.1 or one-tenth.
In conclusion, the step-by-step process involves evaluating the inner function g(−3), substituting this result into the outer functionf(x), and then simplifying the resulting expression to obtain the final numerical value of 1/10.