given the functions f(x) = sqrt x+1 and g(x) = 6x+a in the xy coordinate plane, y= f[g(x)] passes through the point (3,5) . what is the value of a ?
I somehow think you meant
f(x) = √(x+1)
then f(g(x)) = √((6x+a) + 1)
if (3,5) lies on it
5 = √(18+a + 1)
25 = a + 19
a = 6
If you meant f(x) = √x + 1
then follow the same steps as above.
To find the value of "a" in the equation y = f[g(x)], where f(x) = √(x+1) and g(x) = 6x + a, we can substitute the given point (3, 5) into the equation and solve for "a".
Step 1: Replace y with 5 and x with 3 in the equation y = f[g(x)].
5 = f[g(3)]
Step 2: Substitute g(3) into the equation.
5 = f[6(3) + a]
Step 3: Simplify the expression inside the square root.
5 = f[18 + a]
Step 4: Substitute f(18 + a) with the given function f(x) = √(x+1).
5 = √(18 + a + 1)
Step 5: Square both sides of the equation to eliminate the square root.
25 = 18 + a + 1
Step 6: Simplify the equation.
25 = 19 + a
Step 7: Solve for "a" by subtracting 19 from both sides of the equation.
a = 25 - 19
Step 8: Calculate the value of "a".
a = 6
Therefore, the value of "a" is 6.