# What is the composition of two functions g and F?

## What is the composition of two functions g and F?

The composition of two functions g and f is the new function we get by performing f ﬁrst, and then performing g. For example, if we let f be the function given by f(x) = x2and let g be the function given by g(x) = x+3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)).

## What is the domain of the composed function GF(X)?

So the composed function gf(x) can be deﬁned only for x ≥ 3 2, and therefore the domain of the function gf is x ≥ 3 2. In general, the domain of a composed function is either the same as the domain of the ﬁrst function, or else lies inside it. If x is a valid input for the composed function

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How do you find the value of f [g(5)]?

First, find the value of f (g (x)). Find f [g (5)] given that, f (x) = 4x + 3 and g (x) = x – 2. Begin by finding the value of f [g (x)]. Now, evaluate f [g (5)] by substituting x in f [g (x)] with 5.

### What is the product of sum(f+g)(x) and difference(f – g)(x)?

Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x) Product (f · g)(x) = f(x) · g(x) Quotient (f / g)(x) = f(x) / g(x), as long as g(x) isn’t zero. The domain of each of these combinations is the intersection of the domain of f and the domain of g. In other words, both functions must be defined at a point for the combination to

### What is the formula for function composition?

Summary 1 “Function Composition” is applying one function to the results of another. 2 (g º f) (x) = g (f (x)), first apply f (), then apply g () 3 We must also respect the domain of the first function 4 Some functions can be de-composed into two (or more) simpler functions. More

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How do you read the composite function g?

The composite function f [g (x)] is read as “f of g of x ”. The function g (x) is called an inner function and the function f (x) is called an outer function. Hence, we can also read f [g (x)] as “the function g is the inner function of the outer function f ”.

## What is the graph of Ax + b?

Because the graph of ax + b is the graph of ax shifted up or down by b –dependingonwhetherb is positive or negative – the graph of ax + b is a straight line that passes through (0,b) ⇥ R2and has slope equal to a. Problem: Graph p(x)=2x+4. Solution: The graph of 2x+4 is the graph of 2x “shifted up” by 4.

## What is the degree of the polynomial function 4x – 8?

The solution for the polynomial function 4x – 8 is 2. In the given example, the highest exponent found is 7 from -2y 7. This means that the degree of this particular polynomial is 7. Have questions on basic mathematical concepts?