F(x) = x2 + 1 f(f(x))
2 answers:
<h3>Answer: f( f(x) ) = x^4 + 2x^2 + 2</h3>
=============================================
Work Shown:
f(x) = x^2 + 1
f(x) = ( x )^2 + 1
f( f(x) ) = ( f(x) )^2 + 1 .. replace every x with f(x)
f( f(x) ) = ( x^2+1 )^2 + 1 .. plug in f(x) = x^2+1
f( f(x) ) = ( x^2+1 )( x^2+1 )+1
f( f(x) ) = y( x^2+1 )+1 .... let y = f(x) = x^2+1
f( f(x) ) = y*x^2+y+1 ... distribute
f( f(x) ) = x^2*( y ) + ( y ) + 1
f( f(x) ) = x^2*( x^2+1 ) + (x^2+1) + 1 .... plug in y = x^2+1
f( f(x) ) = x^4 + x^2 + x^2 + 1 + 1
f( f(x) ) = x^4 + 2x^2 + 2
--------------------------------------
Side note: , the small circle indicates function composition. It's similar to
You might be interested in
The x-coordinate of the point which divide the line segment is 3.
Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.
When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.
To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.
Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).
Now, we will substitute these values in the formula, we get
x=(1/(1+3))(9-1)+1
x=(1/4)(8)+(1)
x=8/4+1
x=3
Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.
Learn about line segments from here brainly.com/question/10240790
#SPJ4
