the functions f and g are such that f(x)= 2x+5/x-4 and G(x)=2x-3
calculate the value of
a)g(4)
b)fg(2)
c)g`1 (7)
To calculate the value of a function for a specific input, substitute that input into the function expression and simplify the expression.
a) To calculate g(4):
Substitute x = 4 into the expression for g(x):
g(4) = 2(4) - 3
g(4) = 8 - 3
g(4) = 5
Therefore, g(4) = 5.
b) To calculate f(g(2)):
First, find the value of g(2):
Substitute x = 2 into the expression for g(x):
g(2) = 2(2) - 3
g(2) = 4 - 3
g(2) = 1
Now substitute g(2) = 1 into the expression for f(x):
f(g(2)) = f(1)
f(x) = 2x + 5 / x - 4
f(1) = 2(1) + 5 / 1 - 4
f(1) = 2 + 5 / -3
f(1) = 7 / -3
Therefore, fg(2) = 7 / -3.
c) To calculate g`(1) (7), which means finding the derivative of g(x) at x = 7:
The given function g(x) = 2x - 3 is already in its simplest form. Since it is a linear function, the derivative is the coefficient of x, which is 2.
Therefore, g`(1) (7) = 2.