Respuesta :
1. f(3)= 2(3^2)+3 = 21
2. Do you mean (x+3)^4 X x^-3 ?
3. 8-12+6x= 6x-4
4. (4x-3)^-1 = 1/(4x-3)
5. So whats the question for 5?
2. Do you mean (x+3)^4 X x^-3 ?
3. 8-12+6x= 6x-4
4. (4x-3)^-1 = 1/(4x-3)
5. So whats the question for 5?
Answer:
[tex]f(3)=21[/tex]
[tex](x^3)^4.x^{-3}=x^{9}[/tex]
[tex]8-3(4-2x)=6x-4[/tex]
[tex]f^{-1}(x)=\frac{1}{4}(x+3)[/tex]
f = {(2, 5), (3, 2) (4, 6), (5, 1), (7, 2)} is a function
Step-by-step explanation:
[tex]\text{Part 1: Given the function }f(x)=2x^2+3[/tex]
we have to find the value of f(3)
[tex]f(x)=2x^2+3[/tex]
Substitute x=3
[tex]f(3)=2(3)^2+3=2\times 9+3=18+3=21[/tex]
[tex]\text{Part 2: Given the expression }(x^3)^4.x^{-3}[/tex]
we have to simplify the above expression
[tex](x^3)^4.x^{-3}[/tex]
[tex]=x^{3\times 4}.x^{-3}[/tex]
[tex]=x^{12}.x^{-3}[/tex]
[tex]=x^{12-3}=x^{9}[/tex]
[tex]\text{Part 3: Given the expression }8-3(4-2x)[/tex]
[tex]8-3(4-2x)[/tex]
[tex]=8-(12-6x)[/tex]
[tex]=8-12+6x=6x-4[/tex]
[tex]\text{Part 4:Given the function }f(x)=4x-3[/tex]
we have to find the [tex]f^{-1}(x)[/tex]
Replace f(x) to y
[tex]y=4x-3[/tex]
To find inverse we have to replace x=y and y=x, we get
[tex]x=4y-3[/tex]
Now solve for y and replace y with [tex]f^{-1}(x)[/tex]
[tex]x+3=4y[/tex]
[tex]y=\frac{1}{4}(x+3)[/tex]
[tex]f^{-1}(x)=\frac{1}{4}(x+3)[/tex]
which is required inverse
[tex]\text{Part 5: If f = {(2, 5), (3, 2) (4, 6), (5, 1), (7, 2)},}[/tex]
we have to find f is function or not.
If one element of domain x has unique image in range i.e in Y set then only f is called function.
Here one maps to unique element
Therefore f is function.
