Verified Answer :
- 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?
Answer:
\(f(3)=21\)
\((x^3)^4.x^{-3}=x^{9}\)
\(8-3(4-2x)=6x-4\)
\(f^{-1}(x)=\frac{1}{4}(x+3)\)
f = {(2, 5), (3, 2) (4, 6), (5, 1), (7, 2)} is a function
Step-by-step explanation:
\(\text{Part 1: Given the function }f(x)=2x^2+3\)
we have to find the value of f(3)
\(f(x)=2x^2+3\)
Substitute x=3
\(f(3)=2(3)^2+3=2\times 9+3=18+3=21\)
\(\text{Part 2: Given the expression }(x^3)^4.x^{-3}\)
we have to simplify the above expression
\((x^3)^4.x^{-3}\)
\(=x^{3\times 4}.x^{-3}\)
\(=x^{12}.x^{-3}\)
\(=x^{12-3}=x^{9}\)
\(\text{Part 3: Given the expression }8-3(4-2x)\)
\(8-3(4-2x)\)
\(=8-(12-6x)\)
\(=8-12+6x=6x-4\)
\(\text{Part 4:Given the function }f(x)=4x-3\)
we have to find the \(f^{-1}(x)\)
Replace f(x) to y
\(y=4x-3\)
To find inverse we have to replace x=y and y=x, we get
\(x=4y-3\)
Now solve for y and replace y with \(f^{-1}(x)\)
\(x+3=4y\)
\(y=\frac{1}{4}(x+3)\)
\(f^{-1}(x)=\frac{1}{4}(x+3)\)
which is required inverse
\(\text{Part 5: If f = {(2, 5), (3, 2) (4, 6), (5, 1), (7, 2)},}\)
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.