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Assume f of x equals 4x plus 8 and g of x equals 5 What is the value of g o f-1?
g(x) = 5. So whatever f(x) or f(-1) is, g of that is going to be 5.
What is gf 4 if f x equals 5x and g x equals 3x - 7?
f(x)=5x, g(x)=3x-7 gf(x)= = g(f(x)) = g(5x) = 3*(5x) - 7 = 15x-7 So gf(4) = 15*4-7=53
What does it mean when two functions are separated by a circle ex f circle g equals?
Conventionally, f o g is a way to represent the operation of function g followed by function f.So for example, suppose f(x) = x + 2 and g(x) = 3xthen f o g (x) = f[g(x)] = f(3x) = 3x + 2Note, though, that the "o" operator is not commutative.g o f (x) = g[f(x)] = g(x + 2) = 3*(x + 2) = 3x + 6 which is not the same as f o g(x).Such "nested" or "chained" functions are particularly useful in calculus (differentation and integration).
What are the rules of differentiation?
While no set of rules can handle differentiating every expression, the following should help. For all of the following, assume c and n are constants, f(x) and g(x) are functions of x, and f'(x) and g'(x) mean the derivative of f and g respectively. Constant derivative rule:d/dx(c)=0 Constant multiple rule:d/dx(c*f(x))=c*f'(x) Sum and Difference Rule:d/dx(f(x)±g(x))=f'(x)±g'(x) Power rule:d/dx(xn)=n*xn-1 Product rule:d/dx(f(x)*g(x))=f'(x)*g(x) + g'(x)*f(x) Quotient rule:d/dx(f(x)/g(x))=(f'(x)*g(x)-g'(x)*f(x))/f(x)² Chain rule:d/dx(f(g(x))= f'(g(x))*g'(x)
If f-1(x)g(x) inverse then the domain of g(x) the range of f(x)?
If f(x) is the inverse of g(x) then the domain of g(x) and the range of f(x) are the same.
