Can someone show me how to do this?
let f(x)=x^2+3x-1 and g(x)=x^3+4x^2+1
do what?
Its a unit in algebra of functions and i dont know how to solve it
But you did not say what you want to do with the two functions
add them?
multiply them ?
another idea might be composition.
(f◦g)(x) = f(g) = g^2+3g-1
= (x^3+4x^2+1)^2+3(x^3+4x^2+1)-1
= x^6+8x^5+16x^4+5x^3+20x^2+3
(g◦f)(x) = g(f) = f^3+4f^2+1
= (x^2+3x-1)^3+4(x^2+3x-1)^2+1
= x^6+9x^5+28x^4+33x^3+4x^2-15x+4
I was afraid it might be that :)
To find the sum of two functions, f(x) and g(x), you simply add the corresponding terms of the functions.
In this case, we have f(x) = x^2 + 3x - 1 and g(x) = x^3 + 4x^2 + 1.
To find their sum, add the like terms together.
f(x) + g(x) = (x^2 + 3x - 1) + (x^3 + 4x^2 + 1)
First, combine the terms with the same exponent:
= x^3 + (x^2 + 4x^2) + (3x) + (-1 + 1)
Next, simplify the expression by combining like terms:
= x^3 + 5x^2 + 3x
So, their sum is f(x) + g(x) = x^3 + 5x^2 + 3x.