Let #f(x)= 1-x^3# and #g(x)= 1/x#, how do you find each of the compositions?
To find the composition of (f) and (g), denoted as ((f \circ g)(x)), and the composition of (g) and (f), denoted as ((g \circ f)(x)), follow these steps:
-
Finding (f \circ g): ((f \circ g)(x) = f(g(x))) Substitute (g(x)) into (f(x)) to get: ((f \circ g)(x) = f(1/x)) Then, replace (x) in (f(x)) with (1/x): ((f \circ g)(x) = 1 - (1/x)^3) Simplify the expression: ((f \circ g)(x) = 1 - \frac{1}{x^3})
-
Finding (g \circ f): ((g \circ f)(x) = g(f(x))) Substitute (f(x)) into (g(x)) to get: ((g \circ f)(x) = g(1-x^3)) Then, replace (x) in (g(x)) with (1-x^3): ((g \circ f)(x) = \frac{1}{1-x^3})
Therefore, the compositions are: ((f \circ g)(x) = 1 - \frac{1}{x^3}) ((g \circ f)(x) = \frac{1}{1-x^3})
By signing up, you agree to our Terms of Service and Privacy Policy
Think of the
Similarly,
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you find the asymptotes for #ln(x^2 + 1)#?
- How do you find [g of h](x) if #g(x)=8-2x# and #h(x)=3x#?
- How do you find the Vertical, Horizontal, and Oblique Asymptote given #y= (x + 1) / (2x - 4)#?
- How do you find the asymptotes for # f(x)=xe^-x#?
- How do you state the domain and range of #f(x)=x^2-2#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7