Write a function formula for g using the function f. g(x)=

Write a function formula for f using the function g.
f(x)=

a). g(x) = f(x - 2) - 1

b). f(x) = g(x + 2) + 1

Step-by-step explanation:

From the graph attached,

There are two observations:

1). Function 'f' has been shifted by 2 units right and 1 unit down to form image function 'g'.

2). Function 'g' has been shifted 2 units left and 1 unit up to form image function 'f'.

Equation of the quadratic function 'f' is,

f(x) = x²

Equation of function 'g'.

g(x) = (x - 2)² - 1

Therefore, both the functions can be defined as,

a). g(x) = f(x - 2) - 1

b). f(x) = g(x + 2) + 1

the balance is found at the link

step-by-step explanation: